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Many techniques

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Sat Dec 01, 2007 8:05 pm    Post subject: Many techniques Reply with quote

I needed a variety of techniques to unravel this one,
including x-wing, xy-wing, xy-wing plus coloring, xy-chain.
Anyone see a neater path?

Earl


Code:

+-------+-------+-------+
| . . . | . . 1 | 7 . . |
| . 9 2 | 4 . . | . 3 . |
| 4 . 1 | . . 3 | 2 9 . |
+-------+-------+-------+
| 5 . 3 | . 8 . | . 4 . |
| . . . | 5 . 4 | . . . |
| . 8 . | . 3 . | 6 . 5 |
+-------+-------+-------+
| . 1 5 | 6 . . | 4 . 3 |
| . 3 . | . . 2 | 1 5 . |
| . . 7 | 3 . . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Dec 01, 2007 9:59 pm    Post subject: Reply with quote

Medusa wrap again:
I just colored that long long chain of "8"s (only partially shown) and medusa-ed into 6.
In this position:
Code:

+--------------------------+--------------------------+--------------------------+
| 3       5       6g8r     | 29      29      1        | 7       6r8     4        |
| 78g     9       2        | 4       67      678      | 5       3       1        |
| 4       67      1        | 78      5       3        | 2       9       68       |
+--------------------------+--------------------------+--------------------------+
| 5       267     3        | 1       8       67       | 9       4       27       |
| 1679    267     69       | 5       2679    4        | 3       1278    278      |
| 179     8       4        | 279     3       79       | 6       127     5        |
+--------------------------+--------------------------+--------------------------+
| 28r9    1       5        | 6       79      789      | 4       27      3        |
| 69      3       689      | 789     4       2        | 1       5       679      |
| 269     4       7        | 3       1       5        | 8       2r6g    269      |
+--------------------------+--------------------------+--------------------------+

Look at row 7.
If red is true, then r7c1<>2 (because red 8 in r7c1)
AND
if red is true, then r7c8<>2 (because red 2 in r9c8)

Since (under this assumption that red is true) there are no "2"s left in row 7, red must be false. There are tons of cells connected to those red "8"s - the puzzle is solved.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat Dec 01, 2007 11:34 pm    Post subject: Reply with quote

Quote:
Medusa wrap again:


I have a lot to learn.

Keith
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sun Dec 02, 2007 1:30 am    Post subject: Reply with quote

You can get to a contradiction even faster (without using the X-Wing on <8>, which isn't necessary for nataraj's contradiction either) by noting the potential {27} UR in R45C29. If R3C2 is <6>, then R5C9 must be <8> to avoid the DP, creating a second <6> in R2 at C9. So, R3C2 is <7>.

(That's twice in as many days that I've found a DP useful in Medusa coloring!)

After setting R3C2 to <7>, there is a {17} UR in R56C18 that removes <2> from R4C9 and solves the puzzle.
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